Math Problem Statement
Given the following matrix B = [[4, 1], [2, 3]], find the eigenvalues of matrix B and the corresponding eigenvectors for each eigenvalue.
Solution
For the given matrix :
-
The eigenvalues of matrix are:
-
The corresponding eigenvectors for each eigenvalue are:
- For , the eigenvector is
- For , the eigenvector is
Would you like more details or have any questions?
Here are 5 related questions you might explore:
- How do you verify the correctness of eigenvalues and eigenvectors?
- What is the significance of eigenvalues in practical applications?
- Can you calculate the determinant of matrix using its eigenvalues?
- What does it mean if a matrix has repeated eigenvalues?
- How do eigenvectors relate to diagonalization of a matrix?
Tip: Eigenvectors corresponding to distinct eigenvalues are always linearly independent.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Eigenvalues
Eigenvectors
Matrices
Formulas
det(B - λI) = 0 for eigenvalues
(B - λI)v = 0 for eigenvectors
Theorems
Eigenvalue Theorem
Determinant for Eigenvalues
Suitable Grade Level
Undergraduate - Linear Algebra